Question 31 of 44intermediate🔧 ApplyShort Answer3 marks

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

Correct Answer

The sum of first 22 terms is 1661.

Exercise: EXERCISE 5.3 | Q: 7 | (Page Page 21)
For More Understanding

Explanation

This question requires finding the sum of an AP when the common difference and the last term are given. From the textbook context, we use the formula for nth term aₙ = a + (n-1)d to find the first term, and then use the sum formula Sₙ = n/2[2a + (n-1)d]. Alternatively, once we find 'a', we can use Sₙ = n/2(a + l) where l is the last term.

Solution Steps

  1. Step 1: Find the first term 'a' using the nth term formula. Given: d = 7, a₂₂ = 149, n = 22 Using aₙ = a + (n-1)d a₂₂ = a + (22-1) × 7 149 = a + 21×721 \times 7 149 = a + 147 a = 149 - 147 = 2

  2. Step 2: Find the sum of first 22 terms. Using Sₙ = n/2[2a + (n-1)d] S₂₂ = 22/2[2×22 \times 2 + (22-1) × 7] S₂₂ = 11[4 + 21×721 \times 7] S₂₂ = 11[4 + 147] S₂₂ = 11×15111 \times 151 S₂₂ = 1661

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